Using the concept of drift velocity, show that the resistivity of a conductor is ρ = m/(ne²τ). On what factors does it depend?

How to lay out the answer. Follow the frame, then write it in your own words.

1 · Write the starting relations. v_d = eEτ/m and I = neAv_d.
2 · Combine them. I = (ne²τ/m)AE, so j = I/A = σE with σ = ne²τ/m.
3 · Bring in V and l. E = V/l and j = I/A give V = (m/(ne²τ))(l/A)I. Compare with V = IR = ρ(l/A)I.
4 · Draw the diagram. [Wire of length l and area A joined to a cell; E arrow along the wire, electron drift arrow opposite to it]
5 · State the factors. ρ depends on n and τ, so on the material and its temperature, not on l or A.
6 · Real life. That is why copper wires of any thickness share one ρ, while nichrome's ρ is about 60 times larger.
7 · Close in one line. So, ρ = m/(ne²τ).

Scoring tip: Finish by naming both factors, n and τ, and say that the shape of the wire does not affect ρ.